Equilibrium coupled

Another factor that can possibly affect the redox potential in biological systems is the presence of secondary chelating agents that can participate in coupled equilibria (3). When other chelators are present, coupled equilibria involving iron-siderophore redox occur and a secondary ligand will cause the siderophore complex effective redox potential to shift. The decrease in stability of the iron-siderophore complex upon reduction results in a more facile release of the iron. Upon release, the iron(II) is available for complexation by the secondary ligand, which results in a corresponding shift in the redox equilibrium toward production of iron(II). In cases where iron(II) is stabilized by the secondary chelators, there is a shift in the redox potential to more positive values, as shown in Eqs. (42)—(45). 

Limestone and marble are building materials whose main constituent is calcite, the common crystalline form of calcium carbonate. This mineral is not very soluble in neutral or basic solution (Kip = 4.5 X 10-9), but it dissolves in acid by virtue of two coupled equilibria, in which the reactions have a species in common—carbonate in this case ... 

Carbonate produced in the first reaction is protonated to form bicarbonate in the second reaction. Le Chatelicr s principle tells us that, if we remove a product of the first reaction, we will draw the reaction to the right, making calcite more soluble. This chapter deals with coupled equilibria in chemical systems. 

Coupled equilibria are reversible reactions that have a species in common. Therefore each reaction has an effect on the other. 

Let s see, in pure water the hydrogen ion concentration is 1.0 x 10-7 M. Okay, you say. So let s just add the 1.0 x 10"8 M from the HC1 to the 1.0 x 10-7 M from the water. But that doesn t work, because the introduction of H+ from HC1 impacts the self-ionization of water. According to Le Chatelier s principle, the position of the equilibrium will be shifted to the left, because we are adding a product. Many biological systems are coupled equilibria, so if you change one, you change them all. If you want to solve one system, you have to solve all of them simultaneously, because they are all interconnected. 

Thermal and/or photochemical electron transfer within the CT (precursor) complex generates the ion pair D, A as caged or freely diffusive ion-radicals. Most important from a synthetic point of view are the processes by which highly reactive ion-radicals undergo further irreversible transformation resulting in new (thermodynamically stable) products. In other words, the formation of the (precursor) CT complex and electron transfer act in tandem as a coupled set of pre-equilibria. The resultant ion-radical pair can undergo a subsequent (irreversible) transformation (with rate constant fcf) or back ET (Iibi t), which represent the basis for the ET paradigm and drive the coupled equilibria towards the products (P) [4], i.e. ... 

For a trap free situation the term [v ] simplifies to 2, otherwise to 2%B (cf. Section VI.4.//.).175 The r.h.s. term in is obviously exactly the term Wo/co discussed for D 5. Other mechanistic cases are more difficult to handle, especially if the rds does not refer to x = 0 and coupled equilibria have to be taken account of however, the results are comparable. 

Fig. 9 Molecular selection in coupled equilibria through the self-replication of a specific mesos-tructure. (a) Concentration of imines 1A and 7A vs time starting from an equimolar mixture of 1, 7, and A (c = 50 mM each) in CD3CN and, after reaching the thermodynamic equilibrium, by changing the solvent to pure D20. (b) Concentration of imines 1A and 7A vs time starting from an equimolar mixture of 1, 7, and A in D20 (c = 50 mM each). (Reproduced from [46])...

The analysis of coupled equilibria is the most complex problem that is considered in this chapter. It may seem surprising that such apparently straightforward systems like those shown in Eqns. 9.26 and 9.44 should present such great difficulties in analysis, the more so because it is a trivial matter to calculate the equilibrium constants, if the concentrations of the various species are known. However, that situation arises very rarely for several reasons ... 

Thus the solution concentration of complex is fixed by the coupled equilibria. This presents an unusual and interesting condition. 

Many real-world applications of chemistry and biochemistry involve fairly complex sets of reactions occurring in sequence and/or in parallel. Each of these individual reactions is governed by its own equilibrium constant. How do we describe the overall progress of the entire coupled set of reactions We write all the involved equilibrium expressions and treat them as a set of simultaneous algebraic equations, because the concentrations of various chemical species appear in several expressions in the set. Examination of relative values of equilibrium constants shows that some reactions dominate the overall coupled set of reactions, and this chemical insight enables mathematical simplifications in the simultaneous equations. We study coupled equilibria in considerable detail in Chapter 15 on acid-base equilibrium. Here, we provide a brief introduction to this topic in the context of an important biochemical reaction. 

Steam reforming of methanol presents a much more intricate reaction mechanism and a considerably more complicated chemistry than the oxidation of carbon monoxide. The reaction can be formally separated into three highly coupled equilibria. 

The kinetics of the protonation of [Ni(SEt)(triphos)]+ (triphos = Ph2PCH2 CH2 2PPh) by [lutH]+ (lut = 2,6-dimethylpyridine) is consistent with a mechanism comprising two coupled equilibria [44], as shown in Equation (4). Initial protonation occurs at the sulfur. This is followed by the intramolecular equilibration of the proton between the sulfur and nickel sites. 

The opening of this chapter gave an example of coupled equilibria in which calcium carbonate dissolves and the resulting bicarbonate reacts with H. The second... 

For systems with coupled equilibria, an overall relaxation... 

Fersht (9) has shown that CT exist in solution as an equilibrium between active and inactive enzyme. The active molecule contains an intact salt bridge close to the substrate binding site. Alkaline pH destabilizes the salt bridge. Proflavin, an active site inhibitor of CT, binds only to the active molecule. The rate of reconstitution of the salt bridge is in the stopped-flow range. From the amplitude the equilibrium constant of the process can be obtained. The system can be described by two coupled equilibria P... 

However, these four coupled equilibria from Scheme 12.1 are not the full story. Boronic acids readily form stable complexes with buffer conjugate bases (phosphate, citrate and imidazole) [20], In fact, both binary boronate-X complexes are formed with Lewis bases (X), as well as ternary boronate-X-saccharide complexes. In some cases, these previously unrecognized species persist into acidic solution and tmder some stoichiometric conditions they can be the dominant components of the solution. These complexes suppress the boronate and boronic acid concentrations, leading to a decrease in the measured apparent formation constants (f pp). As a consequence, the scope of the simple diol-boronate recognition system is greatly expanded over the simple picture of Scheme 12.1. 

Three relaxation processes observed during the Q-switched laser photolysis of dibromo-[l,3-bis(diphenylphosphino)propane]nickel(ii) in acetonitrile have been assigned " to the relaxation of coupled equilibria involving planar and tetrahedral isomers of the complex together with ion pairs and free ions. The kinetics of the rapid square-planar-octahedral interconversion accompanying the addition of two unidentate ligands L to (14) in chlorobenzene are consistent with a two-step mechanism,... 

Reaction (4.7) is a proton-exchange reaction between two acid-base couples. Equilibria (4.3) and (4.4), which represent the definition of acids and bases, are only virtual ones. It is the same thing for the equilibria described in the previous section. 

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